Qubit hardware for electrons on helium

ABSTRACT

Disclosed is a system and a method to use the system that includes a substrate to support a film of liquid helium and an electron subsystem confined by image forces in a direction perpendicular to the surface of the film, a side gate to electrostatically define a boundary of the electron subsystem, a trap gate to electrostatically define an electron trap located outside the boundary of the electron subsystem, and a load gate to selectively open and close access from the electron subsystem to the electron trap, wherein to open access to the electron trap is to apply a first load gate voltage to the load gate to allow the electrons to access the electron trap, and wherein to close access to the electron trap is to apply a second load gate voltage to the load gate to prevent the electrons from accessing the electron trap.

RELATED APPLICATIONS

This application claims the benefit of U.S. Provisional Application No.62/825,466, filed Mar. 28, 2019, the entire contents of which is beingincorporated herein by reference.

TECHNICAL FIELD

The instant specification generally relates to systems and methods forcreating qubit hardware and qubit control and readout mechanisms forquantum computing. More specifically, the instant specification relatesto producing qubits by confining, inside electrostatic traps, electronsresiding near a surface of liquid helium and to quantum control andreadout of such qubits by probing quantum states of the trappedelectrons with electromagnetic wave signals.

BACKGROUND

Quantum computing is a technology that utilizes quantum bits(qubits)—quantum systems that can be in a superposition state α|0

+β|1

of two quantum states, |0

and |1

, with continuously varying parameters α and β, unlike classical bitswhich always remain in one of the two classical states, 0 or 1.Operation of a quantum computer may include preparation of a qubitstate, quantum entanglement of two or more separate qubits, quantumevolution of the system of entangled qubits in accord with a quantumalgorithm (code) tailored to a particular task being solved, quantumreadout of the end state of the entangled qubits, and—given theintrinsically probabilistic nature of quantum systems—error-correctionmechanisms. Quantum computers can be superior to classical computers fora number of problems (such as prime number factorization) that would notbe practicable on classical computers or that would requireexponentially-large resources. Despite various proposed realizations ofqubits and readout methods, reliable implementation of quantum computingrepresents an outstanding technological challenge. To be feasible foractual quantum computations, qubits should not have additional degreesof freedom that could affect coherence of quantum states of qubits. Atthe same time, an external coupling to individual qubits should bepossible for the preparation of initial states of qubits and for thereadout of their final states. Qubits should be able to retain theirquantum coherence for times that are sufficiently long for the initialstate preparation, quantum algorithm execution, and the final statereadout. The ease and reliability of readout methods remain asignificant bottleneck for the ongoing quantum computational efforts.For the aforementioned reasons, development of realistic qubits andreadout methods is of significant technological importance.

DESCRIPTION OF DRAWINGS

Aspects and implementations of the present disclosure will be understoodmore fully from the detailed description given below and from theaccompanying drawings of various aspects and implementations of thedisclosure, which, however, should not be taken to limit the disclosureto the specific aspects or implementations, but are presented forexplanation and understanding purposes only.

FIG. 1 illustrates schematically an exemplary system that may serve as areservoir of electrons for qubits and that uses liquid helium andelectrostatic gates to facilitate electron confinement, according to oneimplementation.

FIG. 2 illustrates schematically an exemplary system that may realizeelectron traps and that uses liquid helium and electrostatic gates tofacilitate electron confinement, according to one implementation.

FIG. 3 illustrates schematically an exemplary electron loading protocolfor adjusting the number of electrons in an electron trap, according toone implementation.

FIG. 4 is a schematic block diagram illustrating an exemplaryimplementation and components of a system that may implement microwaveand radio frequency single electron transistor-based readout and controlof qubits.

FIG. 5 illustrates schematically an exemplary implementation of anelectronic trap for creating a qubit that uses the lateral motion of atrapped electron.

FIG. 6 illustrates an exemplary spectrum of energy levels of an electronin an electronic trap that uses the lateral motion of a trappedelectron, in one exemplary implementation of a single-electron qubit.

FIG. 7 is a flow diagram illustrating an exemplary implementation of amethod to create and populate an electron trap from a subsystem ofelectrons floating on the surface of a helium film, in one exemplaryimplementation.

FIG. 8 is a flow diagram illustrating an exemplary implementation of amethod to readout, using a radio frequency input signal, a state of aqubit capacitively coupled to a microwave resonator circuit.

FIG. 9 depicts a block diagram of a classical computer system operatingin accordance with one or more aspects of the present disclosure.

DETAILED DESCRIPTION

Aspects of the present disclosure are directed at implementations ofqubits based on surface state electrons and the associated readout andcontrol systems and methods for quantum computation. In some instances,surface state electrons may be implemented using electrons residing neara surface of liquid helium and held to the vicinity of such surface byelectrostatic image forces of attraction to helium. Electrostatic gatesmay be used to confine electrons to a bounded area and further toimplement electron traps outside the bounded area to trap a small numberof electrons therein. The number of electrons trapped in this manner maybe controlled by electrostatic gating and, in some implementations, maybe equal to one. Such individual electrons may be used as qubits. Thequantum states of a qubit, |0

and |1

, may be realized, for example, as a ground state and an excited stateof an electron in the trap. In some implementations, the quantum statesof the qubit may be vertical Rydberg motional states of the electronfloating on the surface of liquid helium. In other implementations, thequantum states of the qubit may be due to a quantized lateral motion ofthe electron inside an engineered electrostatic trap. In yet otherimplementations, a hybrid double qubit may be formed by coupling theout-of-plane and in-plane motion of the electron in the trap. In theseimplementations two qubits with large frequency separation are formedfrom each trapped electron.

Aspects of the present disclosure are also directed at variouscomponents (and their assembly) of a system for implementation ofquantum computing, such as single-electron qubits, electrostatic traps,and associated microwave control and radio-frequency (RF) control andreadout electronics with post processing which uses a classical digitalcomputer. In some implementations, the RF readout of a system containinga qubit or multiple qubits may be performed by preparing an input RFsignal having a frequency tuned to an energy difference between the twoquantum states of the qubit, transmitting the input signal to amicrowave resonator circuit that includes the system containing qubitsas a capacitive element, and detecting a response of the microwaveresonator circuit. The components described herein may be used forperforming single and two-qubit gate operations for universal quantumcomputation. The system and components described herein, when scaled tomultiple qubits (e.g., ˜100 qubits), may be used for unique noisyintermediate scale quantum (NISQ) computation. The system and componentsdescribed herein may be used for further developments in noisereduction, qubit entanglement, and improved qubit coherence forrealization of fully fault-tolerant quantum computing platforms.

FIG. 1 illustrates schematically an exemplary system that may serve as areservoir of electrons for qubits and that uses liquid helium andelectrostatic gates to facilitate electron confinement, according to oneimplementation. Liquid helium in the system 100 may be supported by asubstrate 102. In some implementations, the substrate 102 may be adielectric, e.g., silicon or sapphire. The substrate 102 may support afilm of liquid helium 104. The film of liquid helium may be restrictedlaterally from escaping the substrate 102 by banks 106. In someimplementations, banks 106 may be made of a dielectric material, whichmay be the same as or different from the material of the substrate 102.For example, the banks may be made of SiO_(x) or SiO₂. The banks may bedeposited via thermal evaporation or sputtering. The thickness (height)of the banks 106 may be used to determine the level of liquid film. Insome implementations, the banks may have a thickness 0.2-1 μm, althoughin other implementations the thickness may be below or above this range.In some implementations, the banks 106 may be so positioned as to form amicrochannel of liquid helium, as illustrated in FIG. 1. Themicrochannel (or any other configuration of the helium film 104) may befilled with helium via capillary action using a source of helium (notshown explicitly on FIG. 1). The source of helium may be a low-lyingbulk reservoir of helium.

The helium film 104 may serve as a substrate to support electrons 108floating above the surface of helium. The electrons may be 108 attractedto the surface of helium by long-range image attraction forces, whicharise from interaction of the electron charge with the inducedpolarization of helium. On the other hand, the electrons 108 arerepelled by helium atoms at short range. As a result, the electrons 108may confined near the surface of liquid helium at distances of the orderof 50-100 Å from the surface and have a binding energy of the order of 1meV. The spectrum of the electrons due to image force binding may be ofthe Rydberg type. A bottom gate (electrode) 110 may be located on top ofthe substrate 102. The bottom gate 110 may extend over the entire widthand length of the system, in some implementations. In otherimplementations, the bottom gate may underlie only a part of the system.The bottom gate 110 may be made of a conducting material so that when adirect current (dc) voltage signal is applied to the bottom gate 110,the entire bottom gate 110 acquires the same electric potential. In someimplementations, the electrons 108 may be initially deposited on thesurface of helium by thermionic emission from a filament (e.g., atungsten filament) located near (e.g., above the helium film). In otherimplementations, electrons may be produced via field emission or viaphotoemission. The bottom gate 110 may also be used to control thedensity of electrons. By varying the potential on the bottom gate 110,an optimal density of the electrons 108 on the surface of helium may beachieved. For example, by decreasing the potential on the bottom gate110, a fraction of the electrons 108 may be pushed away. Conversely,upon increasing the potential on the bottom gate 110, the system 100 maybe capable of keeping more of the electrons 108. At high density of theelectrons 108, the electrons 108 may be in a state of Wigner solid witha regular spatial arrangement, as schematically illustrated in FIG. 1.At low densities, the electrons 108 may form an electron liquid state.

Further control over the electrons 108 may be achieved by one or moretop gates (electrodes) 112 which may be fabricated on top of theinsulating banks 106. The top gate(s) 112 may constrict the motion ofthe electrons along the surface of liquid helium 104 by means of alateral electrostatic confinement. For example, by applying a lower(e.g., negative) voltage to a pair of the top gates 112, it may bepossible to squeeze the electron channel together in the lateraldirection. Conversely, by increasing the voltage applied to the topgates 112, the lateral spread of the electron channel may be increased.To control the lateral spread and motion of the electrons 108 (e.g.,along the channel), additional gates (not explicitly shown in FIG. 1)may be used. The top gate 112 (as well as the bottom gate 110 and/orother gates) may be created from a variety of conducting materials. Forexample, the gates may be made of 5 nm of Ti and 45 nm of Au, in oneimplementation, but other designs of the gates are possible in otherimplementations. The gates may be thermally evaporated or sputtered ontothe underlying substrate (e.g., a silicon or sapphire) banks 106, asillustrated by way of example in FIG. 1.

The system 100 shown in FIG. 1 may be designed and manufactured in avariety of implementations. Some of the components shown in FIG. 1 maybe optional. In some implementations, the system 100 may be mountedinside a cryostat (not shown) to sustain consistently low temperatures.The system 100 in the cryostat may be kept at temperatures below theboiling point of helium, 4.2 K. In some implementations, the system 100may be kept at temperatures below ⁴He superfluid transition temperature,2.17 K. In some implementations, the system may be kept at significantlylower temperatures, for example below ³He superfluid transitiontemperature 0.0025 K. In some implementations, cryogen-free ³He-⁴Hedilution refrigerator may be used to achieve temperatures below 0.001 K.At such temperatures, spontaneous thermal transitions between differentRydberg electron states of the vertical confinement may be largelyfrozen out. The surface tension of the liquid helium film 104 may play astabilizing role and keep the electrons 108 at fixed distances fromvarious additional readout and control electrodes, which may befabricated within the system (see below). The stability of the surfaceof helium film 104 may be further controlled by, for example,introducing controlled amounts of the ³He isotope, which has arelatively larger viscosity compared with the ⁴He isotope.

FIG. 2 illustrates schematically an exemplary system 200 that mayrealize electron traps and that uses liquid helium and electrostaticgates to facilitate electron confinement, according to oneimplementation. The system 200 may use some of the concepts illustratedin FIG. 1. Some of the components of the system 200 may correspond tothe component of the system 100. In particular, the components denotedby numbers that differ by the first digit (e.g., 1XY and 2XY) may be thesame or similar in the two systems. Liquid helium in the system 200 maybe supported by a substrate 202. A bottom gate 210 may be deposited ontop of the substrate 202. Liquid helium (not shown explicitly) may beplaced on top of the substrate 202 and/or the bottom gate 210 and form afilm, similar to FIG. 1. The liquid helium film may be supportedlaterally by a set of (e.g., dielectric) banks similar to the banks 106of FIG. 1. In some implementations, the banks may partition liquidhelium into separate reservoirs. The reservoirs may extend over most ofthe lateral dimensions of the system 200, in some implementations. Inother implementations, the reservoirs may extend only over a part of thesystem 200. In some implementations, the reservoirs may be broken into anumber of parallel microchannels. The liquid helium may support anelectron subsystem of the electrons confined in the vertical direction(perpendicular to the surface of helium) by electrostatic image forces,as explained above in relation to FIG. 1. Conducting guard electrodes212 may be deposited above the insulating banks. In someimplementations, the guard electrodes 212 may replicate the map of theunderlying insulating banks. In some implementations, the geometry ofthe guard electrodes 212 may be different from that of the insulatingbanks. The guard electrodes 212 may be formed by the top gate(s). Insome implementations, the guard electrodes 212 may be equipotential. Inother implementations, the guard electrodes 112 may consist of aplurality of disconnected elements so that different potentials(voltages) may be applied to their various parts separately.

In a specific realization schematically illustrated in FIG. 2 (leftpanel) the system 200 has two relatively large regions, the leftreservoir 214 and the right reservoir 216, each containing 20-25microchannel structures. For example, the microchannel structures mayhave a relatively large length (e.g., ˜700 μm, in one implementation).The left reservoir 214 and the right reservoir 216 may define aplurality of electron microchannels, as explained above. The reservoirs214 and 216 may ultimately serve as the electron reservoirs for loadingthe electrons into the electron traps. The system 200 may furtherinclude a plurality of side gates, such as a side gate 218 and a sidegate 220. The side gates 218 and 220 may be electrically isolated fromthe guard electrodes 212 and from each other. In some implementations,the side gates may be separately biased with different electricpotentials. The side gates may define a central microchannel 222 asillustrated by the exploded view of FIG. 2 (central panel). The centralmicrochannel may have a shorter length compared with the dimensions ofthe reservoirs 214 and 216. In some implementations, the length of thecentral microchannel 222 may be 100-200 μm. The density of electrons inthe central microchannel 216 may be controlled, via capacitive coupling,by the voltage applied to the bottom gate 224 whereas the effectivewidth of electrons, which they occupy in central microchannel 222 may befurther controlled with the voltage(s) applied to the side gates 218 and220. To characterize the properties of the obtained electron subsystem,electric transport measurements (such as low and audio frequencyconductivity and compressibility measurements, current-voltagecharacteristics, measurements to determine electron density, etc.) incombination with finite element simulations may be performed todetermine the electrochemical potential φ_(e), the areal electrondensity ns, and/or other quantities. In some implementations, thetransport measurements may be performed by applying a voltage biasbetween the left and right parts of the reservoir electrode 210 so thatthe electric current of electrons occurs only across the centralmicrochannel 222. In other implementations, a voltage bias may beapplied across the microchannels of the left reservoir 214 (or the rightreservoir 216), with the electric current flowing along some or all ofthe microchannels, depending on the specific geometry of driveelectrodes. The drive electrodes may include the guard electrode 212 orseparate additional electrodes (not shown explicitly in FIG. 2).

The electrons floating above the surface of helium in the centralmicrochannel 222 may serve as a source of electrons for the electrontraps 226 shown in FIG. 2 (blowout view, right panel). The electricfield produced by a (voltage-biased) side gate 218 (and side gate 220)may induce one or more boundaries for the electrons 108 in the centralmicrochannel 222. The boundary may delineate the limits for the lateralmotion of the electrons 108 floating above the surface of helium in thecentral microchannel 222. A one or more additional control gates 228 maybe located outside this boundary. A positive voltage applied to thecontrol gate(s) 228 may make it energetically favorable for theelectrons from the central microchannel 222 to move to the vicinity ofthe control gate(s) 228. Because the control gate(s) 228 may have anopposite (e.g., positive) voltage compared to the potential on the sidegate 218 (e.g., negative), in some implementations it make beadvantageous to carve out notches in the side gate 218 to lessen thecounteracting effect of the negative side gate potential. In someimplementations, a charge sensor may be located inside the electron trap226. In some implementations the charge sensor may be a quantum chargesensor capable of detecting presence of individual electrons. Forexample, the charge sensor may be a radio frequency single-electrontransistor sensor (RF-SET sensor) 230.

An additional side microchannel leading from the central microchannel222 to the electron trap 226 may be formed by a load gate 232. The loadgate 232 may selectively open and close access from the electronsfloating above the surface of liquid helium to the electron trap 226.For example, when a positive potential is applied to the load gate 232,the electrostatic attraction of the electrons to the load gate may openthe side microchannel to the electrons from the central microchannel 222so that the electrons may fill the electron trap 226. When a negativevoltage is subsequently applied to the load gate, this negative voltagemay severe the side microchannel by building a potential barrier betweenthe central microchannel 222 and the electron trap 226 and trap theelectrons inside the latter. In some implementations, the controlgate(s) 228, the RF-SET sensor 230, and the load gate 232 may be locatedbelow the surface of helium. In some implementations, the controlgate(s) 228, the RF SET sensor 230, and the load gate 232 may be locatedwithin the plane of the bottom gate 224 while remaining electricallyisolated from the bottom gate 224 and from each other by insulatinginserts 234, as illustrated in FIG. 2. In other implementations, atleast some of the control gate(s) 228, the RF-SET sensor 230, the loadgate 232, and the bottom gate 224, and the reservoir electrode 210 maybe located in different planes.

Once the connection between the central microchannel 222 and theelectron trap 226 is severed, the number of electrons trapped inside theelectron trap 226 may be adjusted as may be necessary by controlling thevoltage V_(g) applied to the control gate(s) 228. For example, as thegate voltage V_(g) is decreased, the potential energy of the electronsin the electron trap 226 is increased (as the electron charge isnegative). As a result, some electrons may be squeezed from the electrontrap 226. This process may be continued until the number of electrons inthe electron trap 226 has reached a pre-determined value. In someimplementations related to quantum computing, the predetermined valuemay be equal to one—a situation where a single-electron quantum qubit isrealized. FIG. 3 illustrates an exemplary electron loading protocol foradjusting the number of electrons in the electron trap 226. Shown is adependence 300 of a charge Q inside the electron trap 226 (in units ofthe electron charge) on the applied control gate 228 voltage V_(g) forone specific realization of the system 200 and the electron trap 226.The dependence 300 shown in FIG. 3 is calculated using a finite elementmodeling. The dependence 300 displays characteristic Coulomb blockadeelectron staircase with sharp transitions between states with n and n+1electrons that occur at specific values of voltage V_(g) when theinteraction of the electrons with the control gate 228 is sufficient toovercome the change in the Coulomb energy of the electron repulsioninside the electron trap 226. By adjusting voltage V_(g), as may beindicated by the Coulomb blockade staircase, the number of electrons inthe electron trap 226 may be controlled so that a pre-determined number(e.g., one, two, three, and so on) of the electrons remain in theelectron trap 226.

In some implementations, the process of loading single electrons intothe trapping region may be performed differently, with the severing ofthe loading microchannel performed subsequently to the adjustment of thenumber of the electrons inside the trap 226. For example, the loadingprocess may be performed as follows. Initially, the electrostaticpotential of the electrons in the electron trap 226 and the loadingmicrochannel may be tuned to be more positive than the electrochemicalpotential of the electrons in the reservoirs 214 and 216 and the centralmicrochannel 222. Under these conditions, the electrons may move alongthe loading microchannel into the electron trap 226. The number ofelectrons loaded into the electron trap 226 may be estimated from thefinite element modeling, as described above. Subsequently, the controlgate voltage V_(g) may be swept to negative (or less positive) values.This will decrease the electrostatic potential in the electron trap 226so that the electrons will be depopulated from the electron trap 226 oneby one, as illustrated by FIG. 3. The voltage difference ΔV_(g) requiredto unload one electron from the electron trap 226, according to thefinite element modeling calculations, may vary from one to several tensof mV depending on the geometric size and the shape of the electron trap226 and its electrostatic environment. In addition to mathematicalmodeling, the electron unloading process may be monitored via the RF-SETsensor 230, as explained in more detail below. Once the number of theelectrons in the electron trap 226 has been reduced to one (or anotherpredetermined value), the electrostatic potential along the loadingmicrochannel may be set to negative values by decreasing the voltage onthe loading gate 232. In some implementations, the potential inside theloading microchannel may be made significantly more negative comparedwith the potential inside the electron trap 226 in order to create asufficiently high potential barrier preventing electron escape from theformed qubit back into the central microchannel 222.

The RF-SET sensor 230 (or any other quantum charge sensor) may be ahighly sensitive radio-frequency single-electron transistormicro-fabricated onto an insulating substrate (e.g., the substrate 202)and submerged beneath the liquid helium surface. In someimplementations, a high speed quantum charge sensor may be used as theRF-SET to measure the vertical motional quantum state of an electrontrapped above it (e.g., inside the electron trap 226). In the fullquantum computing system disclosed herein, the RF-SET sensor 230 mayfacilitate readout of the qubit states. To achieve a high operationalspeed of the RF-SET sensor 230, in some implementations, a conventionalSET may be embedded as the capacitive component of a high-frequencymicrowave resonant circuit. Modern RF-SET based charge sensors have ademonstrated sensitivity of up 1×10⁶ μC/√Hz and measurement speedsgreater than 100 MHz. Such high frequencies are sufficiently fast toreadout Bloch sphere oscillations of the qubit and also be high enoughto ensure that the low frequency 1/f noise from background charges isnegligible to the readout performance of the quantum charge sensor. Insome implementations, the charge sensor may be different from theRF-SET-based sensor. For example, the charge sensor may be an offsetcharge sensitive superconducting qubit, or a similar device capable ofdetecting individual electron charges.

Electrons trapped inside a finite region (e.g., the electron trap 226)may have a discrete spectrum of energies. In a qubit realization, aground state of the electron may represent the qubit state |0

whereas one of the excited states, for example, the first excited state,may represent the qubit state |1

. In various implementations, the first excited state may correspond tovarious quantum motions of the electron. For such traps, the firstexcited state |1

of the qubit may be the first excited Rydberg state for the vertical(i.e., perpendicular to the surface of helium) motion of the trappedelectron. This may represent one exemplary implementation of the qubit.In such implementations, the frequency difference between the firstexcited state |1

of the qubit and its ground state |0

may be about 120 GHz (which corresponds to about 0.5 meV in the energydifference). Conversely, in electron traps whose lateral dimensions arelarger than the Bohr radius of Rydberg states, the spacing between theenergy levels corresponding to the lateral motion may be smaller thanthe spacing between the energy levels corresponding to the verticalmotion of the trapped electrons. For such traps, the first excited state|1

of the qubit may be the first excited for the lateral motion of thetrapped electron (e.g., “particle-in-a-box” quantum motion). This mayrepresent another exemplary implementation of the qubit. Depending onthe degree of confinement of the electron in the electron trap 226—whichmay be controlled via, e.g., the geometry and potentials of the controlgates 228—the energy difference between the states of the qubit may bevaried greatly between different implementations. For example, in oneillustrative and non-limiting implementation, the frequency differencebetween the first lateral excited state |1

of the qubit and its ground state |0

may be about 10 GHz. A superposition α|0

+β|1

of two states of the qubit, with quantum amplitudes α and β, may beprepared and controlled (as discussed in more detail below) using radiofrequency or microwave signals by, for example, inducing Rabioscillations of the amplitudes α and β.

In some implementations, both the vertical motion and the lateral motionof the trapped electrons can be used to implement a two-qubit systemusing a single electron. In such implementations, a trapped electron mayhave at least four Eigenstates, such as |↓0

, |↓1

, |↑0

, and |↑1

, where |↓

is a ground state and |↑

is an excited state with respect to the vertical Rydberg motion of thetrapped electron, and |0

is a ground state and |1

is an excited state with respect to the lateral motion of the trappedelectron. Accordingly, the state |↓0

is the ground state of the trapped electron with energy E₀. The state|↓1

may have energy E₀+E₁ that is higher by a first energy difference E₁corresponding to the excited state with respect to the lateral motion.The state |↑0

may have energy E₀+E₂ that is higher by a second energy difference E₂corresponding to the excited state with respect to the vertical motion.Finally, the state |↑1

may have energy E₀+E₁+E₂, corresponding to the exited states withrespect to both motions. A state of such a two-qubit system may be asuperposition A |↓0

+B|↓1

+C|↑0

+D|↑1

of the four states, with quantum amplitudes A, B, C, and D that may beprepared and controlled using a plurality of radiofrequency or microwavesignals, such as a first signal with frequency E₁/h and a second signalwith frequency E₂/h.

It should be noted that the quantum state for such implementations ofthe qubit may have long quantum coherence times sufficient for quantumcomputation purposes and that in situ positioning of electrons on thesurface of liquid helium is feasible. For example, even inimplementations where the energy difference between the states of thequbit is as low as 10 GHz—which corresponds to about 0.5 K on thetemperature scale—thermal decoherence of the qubit may be negligible attypical temperatures ˜10 mK of the modern dilution refrigerators.

It should be noted that a primary difficulty in utilizing the quantizedvertical or lateral motion of trapped electrons on helium as qubits ishow to implement a sufficiently fast control of qubit dynamics andintegration of the readout electronics into qubits in a comprehensivesystem that would allow single or multiple-qubit gate operations.Aspects of the present disclosure describe such implementations for acomplete and cohesive system that may utilize the quantized motion forNISQ or fully fault-tolerant quantum computing.

As described above, an individual qubit (electron) may be placed abovethe RF-SET sensor 230 located near the electron trap 226 defined by thecontrol gates 228. In other implementations, a similar quantum chargesensor (e.g. an offset charge sensitive superconducting qubit, orsimilar device) can be used for qubit readout in place of the RF-SETsensor 230. The electrons may be loaded from the central microchannel222. A single microchannel may support multiple electron traps 226, asillustrated in FIG. 2 (central panel), with each electron trap 226serving as a separate qubit. In some implementations, individual qubitsmay be separately controlled. For example, different control gatevoltages may be applied to the control gates 228 of different electrontraps 226. As a result, the electrons spectra in different traps may notbe the same. For example, adjacent traps may be tuned to have differentfrequencies corresponding to the energy splitting between the two statesof a qubit: e.g., 12.0 GHz, 12.1 GHz, 12.2 GHz, and so on. Accordingly,the response of a targeted qubit may be resonantly probed with aspecific qubit: the first qubit may be resonantly probed with thedriving frequency of 12.0 GHz whereas a signal having the frequency 12.2GHz will resonantly probe a state of the second qubit, and so on.Correspondingly, a tunable single source of radio frequencies may probequantum states of various qubits. In other implementations, the controlgates 228 may receive the same voltage V_(g) but the geometry and layoutof control gates and/or or the side gate 218 may vary from trap to trap.In some implementations, both the voltages on the control gates 228 aswell as the geometry/layout of different traps may vary. In someimplementations, the trap layout and voltages on the control gates 228may be the same but different dc voltages may be applied to RF-SETsensors 230 that are located near (e.g., underneath) the correspondingelectron traps 226. Such different RF-SET voltages varying from trap totrap may be used to Stark-tune the resonant frequencies of each qubitindividually. In some implementations, individual qubits may beselectively tuned into a resonance with one another to facilitatequantum entanglement of various qubits. Two or more qubits may beentangled in this manner. In some implementations, applied control gatevoltages and/or RF-SET voltages may vary with time. For example, suchvoltages may be varied adiabatically, in order to tune the energies ofthe electron states in the traps without inducing quantum transitionsbetween the quantum states of the traps. In some implementations,entanglement between different qubits (e.g., between nearest neighborand next nearest neighbor qubits) may arise from interaction betweentheir charge degrees of freedom. In particular, such interaction mayarise from electric dipole-dipole coupling. The parameters (e.g.,strength and range) of such coupling may be controlled by electrostaticgating and/or Stark shifting of the qubit energy levels, as disclosedabove. In some implementations, long-range entanglement between distantqubits may be achieved by coupling the electrons in the electron traps226 to an underlying resonator bus (for example, by capacitivecoupling). In some implementations, collective charge oscillations ofmultiple qubits (e.g., plasma oscillations) may be used to establish along-range coupling and entanglement of distant qubits.

The components disclosed in reference to FIGS. 2 and 3 may be mounted ona single chip. In some implementations, various components may bemounted on separate chips. For example, a first plurality of qubits maybe mounted on a first chip while a second plurality of qubits may bemounted on a second chip. In some implementations, the first and/orsecond plurality of qubits may have a linear spatial arrangement. Insome implementations, the first and/or second plurality of qubits mayhave a planar spatial arrangement.

FIG. 4 is a schematic block diagram illustrating an exemplaryimplementation and components of a system 400 that may implementmicrowave and radio frequency single electron transistor-based readoutand control of qubits. The system 400 may include a cryostat and an RFcircuit to deliver one or more RF signals to the cryostat. The system400 may include components to prepare RF and microwave signals (e.g.,one or more signal generators, mixers, amplifiers, multipliers, and thelike), signal guides to deliver the prepared signals to a container(e.g., the cryostat) that contains a microwave resonator circuit coupled(e.g., capacitively) to a system of electron qubits, and components todetect a response of the microwave circuit to the prepared signals (suchas RF-SET sensors, tank circuits, directional couplers,analog-to-digital converters, and the like). These elements areexemplary components that may be used for performing electron qubitstate preparation and subsequent readout. In some implementations, aqubit preparation may begin with a signal generator 402 generating acontinuous-wave radio frequency signal (e.g., a sine signal). The signalgenerator 402 may be a variable frequency signal generator that producesa time-varying signal tuned to the resonant frequency of the qubit. Thesignal generator 402 may be an analog synthesizer, a crystal oscillatorsource, a sufficiently fast digital signal source, and so on. In someimplementations, the signal produced by the signal generator 402 may bephase-shifted by a phase shifter 404 to correct for uncontrolled timedelays and spurious phase shifts of the transmitted signal during itspropagation. To produce controlled one and/or two qubit states withsignals generated by the signal generator 402, these control signal maybe appropriately shaped. In some implementations, the control signalsmay be pulse-shaped. These pulsed signals may have accurately controlledduration, phase, and amplitude. In some implementations this may beachieved via single-side band modulation and mixing. For example, thesignal may be provided to the local oscillator input of a microwavemixer 406. The mixer 406 may be an IQ-mixer, in some implementations,while in others a 3-port mixer may be used. The mixer 406 may have an LOinput coupled to the phase shifter 404 and/or the signal generator 402.The mixer 406 may further have an in-phase input and a quadrature inputto receive signals (e.g., pulses) with frequencies (e.g., 10 MHz-1 GHz)that are lower than a qubit resonance frequency, so that when thesesignals are mixed with the signal generated by the single generator 402,a signal having a frequency at the qubit resonance frequency isobtained. In some implementations, the in-phase input of the mixer 406may receive a first signal from a waveform generator 408, and thequadrature input of the mixer 406 may receive a second signal from thewaveform generator 408. In some implementations, the waveform generator408 may be an arbitrary waveform generator (AWG) or a field programmablegate array (FPGA) board source. The mixer 406 may mix the localoscillator input with the signals (e.g., phase-stable pulses) producedby the waveform generator (AWG) 408. The mixer output may be one or moreradio frequency signals (e.g., pulses) of a predetermined duration,phase and amplitude, as controlled by the generator 408. In someimplementations, the signal produced by the signal generator 402 may bea 5-20 GHz signal corresponding to the difference in the lateral-motionenergy levels of qubits intended to be controlled and read out. In someimplementations, the frequency may be further tuned to the frequency ofa specific (e.g., Stark-tuned) qubit (or a plurality of qubits) by themixer 406, e.g., by using appropriate pulses from the AWG 408. Tocompensate for spurious losses during signal transmission, the mixedsignal may be amplified by an amplifier 410 prior to delivering thesignal into the cryostat 420. For example, an amplifier input RF signalmay be transformed by the amplifier 410 into a signal of the samefrequency but higher amplitude, before outputting the amplified RFsignal to the cryostat 420. In some implementations, the prepared andamplified RF output signal may be delivered directly, via a signal guide412 to the cryostat 420 containing a system of qubits (such as thesystem 200, in some implementations). The signal guide 412 may be afiltered and tapered waveguide or a coaxial cable, such as a filteredand attenuated coaxial semi-rigid cable. In some implementations, suchas where both the lateral and the vertical motion of a trapped electronare used to implement a two-qubit system, both the waveguide and thecoaxial cable may be used to deliver signals to the cryostat 420concurrently. In some implementations, the qubit resonant frequency maybe significantly higher than the frequency of the signal output by themixer 406 (and the amplifier 410). For example, this may be in casewhere qubits utilize lateral Rydberg states of the vertical motion ofthe trapped electrons. In such implementations, the signal output by themixer 406 (and the amplifier 410) may be processed by a frequencymultiplier 416 to up-convert the frequency to a target frequency (withthe target frequency corresponding to the energy difference between theeigenstates of a qubit). In some implementations, the up-convertedfrequency may be at least ten times higher the frequency of the signaloutput by the mixer 406 and/or the amplifier 410. For example, asillustrated by way of example and not of limitations in FIG. 4, a 12×multiplier may up-convert the initial frequency 10 GHz into a 120 GHzsignal. The frequency multiplier 416 may be based on standard frequencyextender modules, in some implementation. In other implementations, thefrequency multiplier may operate using mixer-based up-conversion. Theresulting up-converted high frequency signals (e.g., pulses) may then betransmitted to the cryostat 420 through a signal guide 418. The signalguide may be a tapered waveguide. The signal guide 418 may includeadditional filters to filter out spurious signals than may have beenproduced during up-conversion or radiated from regions of the systemhaving higher temperature than the sections of the cryostat, which maybe held at 10 mK.

In some implementations, only one of the signal guides 412 and 418 maybe utilized. For example, when vertical motion of the trapped electronis being used as a qubit, only the signal guide 418 may be used whereasno signal is being transmitted through the signal guide 412. In someimplementations, both the high-frequency signals (e.g., 120 GHz signals,as illustrated) and the low-frequency signals (e.g., 10 GHz signals, asillustrated) may be transmitted concurrently through the signal guides418 and 412, respectively. For example, this may be done if the systemof qubits contains qubits of different types—those that use verticalmotion of trapped electrons and those that use lateral motion of trappedelectrons—and both types of qubits need to be readout (or prepared) atthe same time.

The signal (whether up-converted or not) transmitted to the cryostat 420that may include a system of qubits, may be used to probe a quantumstate of one or more qubits. The quantum state of one or more qubits mayrepresent the result of a prior execution of a quantum code by thesystem of qubits. Upon the completion of the code, the quantum state ofthe system of qubits may need to be readout for subsequent processing ona conventional (classical) computer. The state of a system of multiplequbits may be an entangled combination of quantum states of individualqubits. To determine the properties of such entangled combination, thesystem of qubits may be subjected to one or more pulses of microwaveradiation (prepared as disclosed above) and the state of the system ofqubits at the end of the quantum code execution may be ascertained froma response of the qubits to microwave radiation. In someimplementations, such response may include Rabioscillations—time-dependent evolution of the quantum amplitudesdescribing a superposition of the quantum states |1

and |0

of the qubit. Such Rabi oscillations, in some implementations, may bemeasured via the damping and frequency shift of a microwave resonantcircuit that includes the RF-SET sensor 430 as a probe of the electrontrap 226, as disclosed above (e.g., as RF-SET sensor 230 of the system200). In some implementations, the RF-SET sensor 430 may have two tunneljunctions connected through a central island, as schematically indicatedby the components inside a dashed rectangle SET in FIG. 4. The centralisland may be made of a metal or a semiconductor. In someimplementations, the central island may be made of a superconductingmaterial. In some implementations, the central island may be a quantumdot. The central island of the RF-SET sensor 430 may be capacitivelycoupled to a gate and a gate voltage 431 may be applied therein. Forexample, the gate voltage 431 may be used to tune the state of theRF-SET sensor 430 so that a single conduction electron resides on thecentral island. A bias voltage 433 may further be applied to the RF-SETsensor 430, as illustrated in FIG. 4.

The response detected by the RF-SET 430 may be passed through asufficiently fast analog-to-digital converter (ADC) 432 where theresponse may be sampled and digitized. In some implementations, the ADC432 may be have a speed of ˜0.5-6.4 GS/s or higher. Synchronization ofthe control and measurement scheme may improve operation of qubitsystems. For example, synchronization may be facilitated by a masterclock 434. Additionally, the signal from the RF-SET 430 can be monitoredin either reflection or transmission at the resonant frequency of aresonant circuit 436 using a two-port vector network analyzer (VNA) 441.In one embodiment, the resonant circuit is an LC tank circuit in whichan inductor is coupled in series between the RF-SET sensor 430 and acapacitor is coupled in parallel between the RF-SET sensor 430 andground (or ground potential). The measurement circuit may includeadditional elements, such as a directional coupler 438 for directing thereadout signal from generator 440. In some implementations this couplercan be replaced with a 3-port isolator or a circulator. The signalgenerator 440 may generate RF signals within a broad range of frequency(10-100 MHz) for interrogation of the tank circuit 436 containing theRF-SET, depending on the specific implementation. The master clock 434may be coupled to both the ADC 432, the waveform generator 408, and theRF signal source 440 for synchronization of the qubit preparation andreadout. In some implementations, the master clock 434 may correlatepulses generated by the signal generator 402 and mixer 406 with theoutput received by the ADC 432.

With reference to the qubit realization via vertical Rydberg states oftrapped electrons, the characteristic time scale for the Rabioscillations of such qubits may be within the range of ˜100 MHz-1 GHz,in some implementations. Given the coherence times known in the art,this may allow for up to more than a hundred quantum gate operationswith these qubits. This makes the readout mechanism disclosed herein aviable component of a comprehensive quantum computing system.

In those implementations where the qubits are realized via the quantizedlateral motion of electrons within the electronic traps 226, thefrequency difference between the ground state |0

and the first excited state |1

of such motion (which is the resonant frequency of the qubit) may beengineered (via the geometry of the trap 226 and its control gates 228)to be of the order of 1-10 GHz. In some implementations, the readout ofsuch lateral motional states of qubits may also be accomplished (inaddition to the readout mechanisms disclosed above) by using the RF-SETtechnology together with microwave circuits similar to the circuits thathave been developed for circuit quantum electrodynamic measurements ofsuperconducting circuit-based qubits. The novelty of the conceptsdisclosed herein with regards to incorporation of such circuit-basedimplementations is in the use of specific reservoir and trap designs toensure the formation of well-defined qubit states as well as theintegration of these features with the microwave control and the RF-SETreadout scheme.

Although the above disclosure with reference to FIG. 4 described thequbit readout techniques, the same techniques may be used for qubitcontrol. More specifically, qubits that are initially in the groundstate |0

may be evolved into a desired superposition state α|0

+β|1

(as required by a quantum computation code to be implemented on thesystem of qubits) by inducing the Rabi oscillations in the qubits uponsubjecting them to the pulsed microwave signals according to thetechnique described in relation to FIG. 4.

FIG. 5 illustrates schematically an exemplary implementation 500 of anelectronic trap (e.g., electronic trap 226) for creating a qubit thatuses the lateral motion of a trapped electron. The electronic trap 500may have an asymmetric shape; for example, the trap may be 4 μm long and1 μm wide, in one exemplary non-limiting implementation. The asymmetryof the trap may serve to lift the degeneracy of the excited statescorresponding to the lateral motion of the electron and, therefore, tosuppress decoherence of the state |1

due to virtual transitions to/from another excited state with a closeenergy. FIG. 6 illustrates, by way of example, the energy differencebetween the energy levels of the qubit, E_(n)-E_(m), as a function ofthe voltage applied to the control gate 228, in one specificimplementation. The energy difference shown in FIG. 6 was calculated bynumerically solving Schrodinger's equation for the Eigenstates andEigen-energies of the motion of the trapped electrons. As indicated bythe data 600, the qubit transition frequency for the transition from theground stat to the first excited state, |0

→|1

, can be tuned over a wide range—within approximately 4-8 GHz—bychanging the potential on the control gate 228.

The qubit implementation illustrated by FIG. 6 displays anharmonicity:the energy (or, equivalently, transition frequency) difference E₁-E₀between first excited state and the ground state is different from thedifference E₂-E₁ between the second excited state and the first excitedstate. For the specific illustrative implementation shown in FIG. 6, therange of such anharmonicity is of the order 0.1-0.4 GHz. In someimplementations, such anharmonicities may be advantageous. For example,when the frequency of the readout microwave signals is tuned close tothe difference E₁-E₀, the ensuing Rabi oscillations may be limited tothe transitions between the states |0

and |1

. Accordingly, the same readout microwave signals would be unlikely toinduce transitions between the states |1

→|2

. This may prevent spurious admixture of the higher excited states |2

, |3

. . . , that would result in the qubit decoherence. In someimplementations, the degree of anharmonicity may be controlled by thegeometry of the electron trap to ensure that qubit excitation intohigher excited states is ruled out.

During qubit operations, qubit initialization into the motional groundstate |0

may occurs naturally upon populating the microchannels and electrontraps with electrons, as disclosed above. This may occur because typicaloperating temperatures of the system (˜10 mK) may be significantly lowerthan the qubit transition energy, E₁-E₀. During subsequent qubit controloperations (e.g., gate operations), excitation of qubits into states |1

can be achieved by using pulsed microwave fields tuned to the qubittransition frequencies, as described above in relation to FIG. 4.

FIG. 7 is a flow diagram illustrating an exemplary implementation of amethod 700 to create and populate an electron trap from a subsystem ofelectrons floating on the surface of a helium film, in one exemplaryimplementation. In some implementations, method 700 may be performedusing systems and components disclosed above in relation to FIGS. 1-6.Method 700 may begin with preparing a film of liquid helium that maysupport an electron subsystem of electrons floating near a surface ofthe film (710). For example, method 700 may include preparing asubstrate with microchannels that are filled with liquid (e.g.,superfluid) helium using capillary action of helium. Preparation of thefilm may include populating the electron subsystem with electrons froman electron source, e.g., by thermionic emission from the source.Preparation of the film may also include characterization of theelectron subsystem, for example, by performing measurements to determinethe electrochemical potential of the electron subsystem, the density(e.g., the aerial density of electrons), and/or other quantities of theelectron subsystem. Preparation of the film may also include placingvarious gates near the film of liquid helium. Some of the gates may beelectrically isolated from helium and from the electron subsystem butmay be capacitively coupled to the latter. Some of the gates may be in adirect electric contact with the helium film Some of the gates may bevoltage-biased. Some of the gates may be used to create a boundary ofthe electron subsystem. Some of the gates may be used to define one ormore electron traps outside the boundary, so that the electrons in theelectron traps are spatially (e.g., laterally) separated from the restof the electron subsystem and/or electrons that may reside in otherelectron traps.

Method 700 may continue with applying a first side gate voltage to aside gate to create a boundary of the electron subsystem (720). In someimplementations, the magnitude of the first side gate voltage may beused to control the location and the shape of the boundary. In someimplementations, the side gate may have a plurality of electricallyconnected parts so that a microchannel of liquid helium is formedbetween the parts of the side gate. In some implementations, the sidegate may include a plurality of electrically disconnected parts.Accordingly, the term “a side gate voltage” may include a plurality ofvoltages applied to different parts of the side gate. Method 700 maycontinue with applying a first trap gate voltage to a trap gate tocreate an electron trap located outside the boundary of the electronsubsystem (730). The term “trap gate” includes the control gate(s) 228of FIG. 2. The electron trap may be defined by the electrostaticpotential having a maximum at or near the trap location (so that thepotential energy of negatively charged trapped electrons may have aminimum there). In some implementations, the trap gate may be a singleelectrode surrounding the trap, as illustrated in FIG. 5. In someimplementations, the trap gate may include a plurality of electrodes, asillustrated in FIG. 2 (right panel) with a plurality of different trapgate voltages applied to different electrodes (e.g., control gates 228).In some implementations, no first trap gate voltage may be applied atall: for example, the electron trap may be defined by a specific shapeof the side gate so that a region of an elevated electrostatic potentialis formed outside the boundary of the electron subsystem.

Method 700 may continue with applying a first load gate voltage to aload gate to open access of the electrons of the electron subsystem(740). For example, the first load gate voltage may modify the spatialprofile of the electrostatic potential in such a way as to allow anaccess of electrons from the boundary of the electron subsystem to theelectron trap (e.g., by forming a microchannel between the two regions).In some implementations, no first load gate voltage may be applied atall: for example, the microchannel may be formed due to a specific shapeof the side gate so that a region of an elevated electrostatic potentialexists all the way from the boundary of the electron subsystem towardsthe trap region. Method 700 may continue with applying a second loadgate voltage to the load gate to close access of the electrons of theelectron subsystem to the electron trap (750). For example, the secondload gate voltage may be less positive than the first load gate.Accordingly, the microchannel previously formed between the electrontrap and the boundary of the electronic subsystem may be severed so thatthe electrons are trapped in the electron trap.

Method 700 may continue with applying a second trap gate voltage to thetrap gate to adjust a number of the electrons in the electron trapvoltage (760). More specifically, after the microchannel to the electrontrap is severed, the trap may contain a number of electrons differentfrom a required number of electrons. In some implementations, the secondtrap gate voltage may be lower than the first trap gate voltage. Thismay elevate the potential energy of the electrons in the trap and pushsome of the electrons over the potential barrier back to the electronsubsystem. In particular, decreasing the voltage on the trap gate maycause the system to “walk” down the Coulomb blockade staircase (asillustrated by way of example in FIG. 3). The second trap gate voltagemay be selected in such a way as to keep a predetermined number of theelectrons in the trap, e.g., one, two, three, and so on. In someimplementations, to form a single-electron qubit, the second trap gatevoltage may be so chosen that only one electron remains in the trap(e.g., corresponding to the step Q=1 of the Coulomb blockade staircase).In some implementations, the required second trap voltage may be knownfrom previous calibration measurements. In some implementations,applying the second trap gate voltage may not be performed at all andthe required number of remaining electrons (e.g., Q=1) may be achievedby a proper choice of the first trap gate voltage at block 730 and/orthe first side gate voltage at block 720. In some implementations, afterthe application of the second trap gate voltage and adjusting the numberof trapped electrons is performed, a third trap gate voltage may beapplied (not shown in FIG. 7). The third trap gate voltage may be higher(e.g., more positive) than the second trap gate voltage, so that thedepth of the potential well for the remaining electron(s) in the trap isincreased in order to prevent the remaining electron(s) from escapingthe trap.

Some of the operations of method 700 may not have to be used every timethe method 700 is performed. For example, preparation of the helium filmat block 710 may be performed only once for multiple instances ofapplying gate voltages for electron trapping. In some implementations,as long as the helium film remains stable (or replenished from areservoir), no additional preparation may be needed.

FIG. 8 is a flow diagram illustrating an exemplary implementation of amethod 800 to read out, using a radio frequency input signal, a state ofa qubit capacitively coupled to a microwave resonator circuit. Method800 may begin with preparing a first input signal having a frequencycorresponding to a first energy difference between the Eigenstates of aqubit (810). The Eigenstates of the qubit may correspond to a vertical(perpendicular to the surface of liquid helium) or a lateral (parallelto the surface of liquid helium) motion of the trapped electron. In someimplementations, the first input signal may be prepared with some or allof the radio circuitry components 402, 404, 406, 408, 410, 412, 416, 418shown in FIG. 4. Method 800 may continue with subjecting the qubit tothe prepared first input signal by delivering the first input signal toa microwave resonator circuit containing the qubit as a capacitivecomponent (820). Depending on the energy difference between theEigenstates of the qubit, delivering the first input signal may utilizetransmitting the first input signal to a holder of the qubit (e.g., intothe cryostat) through a coaxial radio-frequency cable or a taperedwaveguide. The qubit may be a part of a microwave resonator circuit. Forexample, the trapped electron(s) of the qubit may be capacitivelycoupled to an RF-SET located in the proximity to the trapped electron,as illustrated in FIGS. 2, 4, and 5. The RF-SET may be included in themicrowave resonator circuit, as illustrated in FIG. 4, in one exemplaryimplementation.

Method 800 may continue with detecting a first response of the microwaveresonator circuit to the first input signal (830). In someimplementations, this may be performed by measuring the impedanceresponse of the microwave resonator circuit—e.g., the frequency shiftand the damping of the circuit. Method 800 may continue with determiningthe state of the qubit from the measured response of the microwaveresonator circuit (840). The first response of the microwave resonatorcircuit may be processed by an analog-to-digital converter and the Rabioscillations of the qubit may be determined using a subsequentprocessing on a classical computer. As a result, the state of thequbit(s) that existed prior to the subjecting it to the input microwavesignal (e.g., upon completion of a quantum code execution) may beascertained.

In some implementations, the method 800 may use multiple signalsconcurrently. For example, while the first input signal may have afrequency corresponding to one of the vertical or a lateral motion ofthe trapped electron, a second input signal may have a frequencycorresponding to the other one of the motions (e.g., lateral orvertical) of the trapped electron. In some implementations, the secondinput signal may be obtained by the multiplier 416 upconverting an RFsignal output by the amplifier 410 and/or mixer 406. Accordingly, twoinput signals may be prepared at block 810. Similarly, at block 820, thequbit may be subjected to the first input signal and the second inputsignal concurrently (or at different, e.g., consecutive, times). In someimplementations, the first input signal may be delivered to themicrowave resonator circuit through a coaxial cable whereas the secondinput signal may be delivered to the microwave resonator circuit througha waveguide (e.g., a tapered waveguide). At block 830, a second responseof the microwave resonator to the second input signal may be detectedtogether with the first response of the microwave resonator to the firstinput signal. At block 840, determining the state of the qubit may beperformed, in some implementations, based on both the first response andthe second response. As a result of performing method 800, a four-bitstate of the qubit may be determined, such as a state of the qubit thatis a superposition of eigenstates |↓0

, |↓1

, |↑0

, and |↑1

.

A method similar to method 800 may be used to prepare a state of thequbit(s) prior to the execution of a quantum code. For example, afterpopulating electron traps (e.g., according to method 700 or some otherequivalent method), the corresponding qubits may be in the ground states|0

. To prepare superposition states α|0

+β|1

(as may be required by a specific quantum computation code to beimplemented on the system of qubits), the qubits may be subjected toappropriately prepared microwave signals in order to induce the Rabioscillations of such amplitude and duration as to drive the qubit(s)into the required superposition states.

A method similar to method 800 may be performed using a plurality ofqubits. For example, a device comprising the plurality of qubits and aplurality of control gates can be capacitively coupled to the microwaveresonator circuit. Various qubits (and/or) control gates qubits may havea linear spatial arrangement (e.g., to be positioned along the sameline) or a planar spatial arrangement. (e.g., may be positioned withinthe same plane). In some implementations, each of the plurality ofqubits may be associated with a respective control gate of the pluralityof control gates. In some implementations, in indication that a targetedqubit is to be read out may be received by a processing device (e.g., acomputing system). A control voltage may be applied to the respectivecontrol gate associated with the targeted qubit to Stark-tune an energydifference between eigenstates of the targeted qubit. The Stark-tuningmay be performed so that the energy difference Δ_(T) between theeigenstates of the targeted qubit is away from the correspondingdifferences A of the eigenstate energies of other qubits (e.g., that thequantity |Δ_(T)−Δ| exceeds an inverse (radiative or non-radiative)lifetime of the qubits). The method may continue with preparing an inputsignal having a frequency corresponding to the energy difference Δ_(T),subjecting the device to the input signal by delivering the input signalinto the microwave resonator circuit, detecting a response of themicrowave resonator circuit to an input signal, and determining thestate of the targeted qubit from the response of the microwave resonatorcircuit.

Methods 700 and 800, as well as other methods that are similar tomethods 700 and/or 800, may be performed by processing logic that mayinclude hardware (e.g., circuitry, dedicated logic, programmable logic,microcode, etc.), software, firmware or a combination thereof. Methods700 and 800 and/or each of its individual functions, routines,subroutines, or operations may be performed by one or more processingunits of a classical computer. In certain implementations, methods 700and 800 may be performed by a single processing thread. Alternatively,methods 700 and 800 may be performed by two or more processing threads,each thread executing one or more individual functions, routines,subroutines, or operations of the method. In an illustrative example,the processing threads implementing methods 700 and 800 may besynchronized. Alternatively, the processing threads implementing methods700 and 800 may be executed asynchronously with respect to each other.Various steps of the methods 700 and 800 may be performed in a differentorder compared to the order shown in FIGS. 7 and 8. Some steps may beperformed concurrently with other steps.

FIG. 9 depicts a block diagram of a classical computer system 900operating in accordance with one or more aspects of the presentdisclosure. For example, the classical computing system 900 mayimplement a classical computing code to be used in preparation andcontrol of the initial state of one or more of qubits, in someimplementations. The computing system 900 may implement some of theoperations illustrated in FIG. 4, in some implementations. The computingsystem 900 may perform processing of response data received from themicrowave resonator circuit and to determine the final states of thequbits that are to be read out. In certain implementations, computersystem 900 may be connected (e.g., via a network, such as a Local AreaNetwork (LAN), an intranet, an extranet, or the Internet) to othercomputer systems. Computer system 900 may operate in the capacity of aserver or a client computer in a client-server environment, or as a peercomputer in a peer-to-peer or distributed network environment. Computersystem 900 may be provided by a personal computer (PC), a tablet PC, aset-top box (STB), a Personal Digital Assistant (PDA), a cellulartelephone, a web appliance, a server, a network router, switch orbridge, or any device capable of executing a set of instructions(sequential or otherwise) that specify actions to be taken by thatdevice. Further, the term “computer” shall include any collection ofcomputers that individually or jointly execute a set (or multiple sets)of instructions to perform any one or more of the methods describedherein.

In a further aspect, the computer system 900 may include a processingdevice 902, a volatile memory 904 (e.g., random access memory (RAM)), anon-volatile memory 906 (e.g., read-only memory (ROM) orelectrically-erasable programmable ROM (EEPROM)), and a data storagedevice 916, which may communicate with each other via a bus 908.

Processing device 902 may be provided by one or more processors such asa general purpose processor (such as, for example, a complex instructionset computing (CISC) microprocessor, a reduced instruction set computing(RISC) microprocessor, a very long instruction word (VLIW)microprocessor, a microprocessor implementing other types of instructionsets, or a microprocessor implementing a combination of types ofinstruction sets) or a specialized processor (such as, for example, anapplication specific integrated circuit (ASIC), a field programmablegate array (FPGA), a digital signal processor (DSP), or a networkprocessor).

Computer system 900 may further include a network interface device 922.Computer system 900 also may include a video display unit 910 (e.g., anLCD), an alphanumeric input device 912 (e.g., a keyboard), a cursorcontrol device 914 (e.g., a mouse), and a signal generation device 920.

Data storage device 916 may include a non-transitory computer-readablestorage medium 924 which may store instructions 926 encoding any one ormore of the methods or functions described herein, includinginstructions to implement a model of detection of adverse employeerelations and potential resignation, in particular, for implementingmethods 700 and 800.

Instructions 926 may also reside, completely or partially, withinvolatile memory 504 and/or within processing device 902 during executionthereof by computer system 500, hence, volatile memory 904 andprocessing device 902 may also constitute machine-readable storagemedia.

While computer-readable storage medium 924 is shown in the illustrativeexamples as a single medium, the term “computer-readable storage medium”shall include a single medium or multiple media (e.g., a centralized ordistributed database, and/or associated caches and servers) that storethe one or more sets of executable instructions. The term“computer-readable storage medium” shall also include any tangiblemedium that is capable of storing or encoding a set of instructions forexecution by a computer that cause the computer to perform any one ormore of the methods described herein. The term “computer-readablestorage medium” shall include, but not be limited to, solid-statememories, optical media, and magnetic media.

The methods, components, and features described herein may beimplemented by discrete hardware components or may be integrated in thefunctionality of other hardware components such as ASICS, FPGAs, DSPs orsimilar devices. In addition, the methods, components, and features maybe implemented by firmware modules or functional circuitry withinhardware devices. Further, the methods, components, and features may beimplemented in any combination of hardware devices and computer programcomponents, or in computer programs.

It should be understood that the above description is intended to beillustrative, and not restrictive. Many other implementation exampleswill be apparent to those of skill in the art upon reading andunderstanding the above description. Although the present disclosuredescribes specific examples, it will be recognized that the systems andmethods of the present disclosure are not limited to the examplesdescribed herein, but may be practiced with modifications within thescope of the appended claims. Accordingly, the specification anddrawings are to be regarded in an illustrative sense rather than arestrictive sense. The scope of the present disclosure should,therefore, be determined with reference to the appended claims, alongwith the full scope of equivalents to which such claims are entitled.

The implementations of methods, hardware, software, firmware or code setforth above may be implemented via instructions or code stored on amachine-accessible, machine readable, computer accessible, or computerreadable medium which are executable by a processing element coupled tomemory. “Memory” includes any mechanism that provides (i.e., storesand/or transmits) information in a form readable by a machine, such as acomputer or electronic system. For example, “memory” includesrandom-access memory (RAM), such as static RAM (SRAM) or dynamic RAM(DRAM); ROM; magnetic or optical storage medium; flash memory devices;electrical storage devices; optical storage devices; acoustical storagedevices, and any type of tangible machine-readable medium suitable forstoring or transmitting electronic instructions or information in a formreadable by a machine (e.g., a computer).

Reference throughout this specification to “one implementation” or “animplementation” means that a particular feature, structure, orcharacteristic described in connection with the implementation isincluded in at least one implementation of the disclosure. Thus, theappearances of the phrases “in one implementation” or “in animplementation” in various places throughout this specification are notnecessarily all referring to the same implementation. Furthermore, theparticular features, structures, or characteristics may be combined inany suitable manner in one or more implementations.

In the foregoing specification, a detailed description has been givenwith reference to specific exemplary implementations. It will, however,be evident that various modifications and changes may be made theretowithout departing from the broader spirit and scope of the disclosure asset forth in the appended claims. The specification and drawings are,accordingly, to be regarded in an illustrative sense rather than arestrictive sense. Furthermore, the foregoing use of implementation,embodiment, and/or other exemplarily language does not necessarily referto the same implementation or the same example, but may refer todifferent and distinct implementations, as well as potentially the sameimplementation.

The words “example” or “exemplary” are used herein to mean serving as anexample, instance or illustration. Any aspect or design described hereinas “example’ or “exemplary” is not necessarily to be construed aspreferred or advantageous over other aspects or designs. Rather, use ofthe words “example” or “exemplary” is intended to present concepts in aconcrete fashion. As used in this application, the term “or” is intendedto mean an inclusive “or” rather than an exclusive “or.” That is, unlessspecified otherwise, or clear from context, “X includes A or B” isintended to mean any of the natural inclusive permutations. That is, ifX includes A; X includes B; or X includes both A and B, then “X includesA or B” is satisfied under any of the foregoing instances. In addition,the articles “a” and “an” as used in this application and the appendedclaims should generally be construed to mean “one or more” unlessspecified otherwise or clear from context to be directed to a singularform. Moreover, use of the term “an embodiment” or “one embodiment” or“an implementation” or “one implementation” throughout is not intendedto mean the same embodiment or implementation unless described as such.Also, the terms “first,” “second,” “third,” “fourth,” etc. as usedherein are meant as labels to distinguish among different elements andmay not necessarily have an ordinal meaning according to their numericaldesignation.

What is claimed is:
 1. A system comprising: a substrate to support afilm of liquid helium, wherein the film of liquid helium is to supportan electron subsystem comprising electrons that are confined, in adirection perpendicular to a surface of the film of liquid helium, byimage forces of electrostatic attraction to the film of liquid helium; aside gate to receive a side gate voltage to electrostatically define aboundary of the electron subsystem; a trap gate to receive a trapvoltage to electrostatically define an electron trap located outside theboundary of the electron subsystem; and a load gate to selectively openand close access from the electron subsystem to the electron trap,wherein to open access of the electron subsystem to the electron trap isto apply a first load gate voltage to the load gate to allow theelectrons of the electron subsystem to access the electron trap, andwherein to close access of the electron subsystem to the electron trapis to apply a second load gate voltage to the load gate to prevent theelectrons of the electron subsystem from accessing the electron trap. 2.The system of claim 1, further comprising a charge sensor capacitivelycoupled to the electron trap.
 3. The system of claim 2, wherein thecharge sensor comprises a single-electron transistor.
 4. The system ofclaim 1, further comprising a radio frequency (RF) circuit to generatean RF signal output to a cryostat, wherein the cryostat comprises thesubstrate, the side gate, the trap gate, and the load gate.
 5. Thesystem of claim 4, wherein the RF circuit comprises an amplifier totransform an amplifier input RF signal into the RF signal output to thecryostat.
 6. The system of claim 5, wherein the RF circuit furthercomprises: a waveform generator to output a first signal and a secondsignal; and a mixer to receive a local oscillator input, the firstsignal and the second signal, wherein the mixer is to output theamplifier input RF signal.
 7. The system of claim 6, wherein an in-phaseinput of the mixer is to receive the first signal and a quadrature inputof the mixer is to receive the second signal.
 8. The system of claim 5,further comprising a coaxial cable to deliver the RF signal output tothe cryostat.
 9. The system of claim 4, wherein the RF circuitcomprises: an amplifier to transform an amplifier input RF signal intoan amplified RF signal; and a multiplier to multiply the amplified RFsignal to obtain the RF signal output to the cryostat.
 10. The system ofclaim 9, further comprising a waveguide to deliver the RF signal outputto the cryostat.
 11. The system of claim 10, wherein the waveguide is atapered waveguide.
 12. The system of claim 4, further comprising acharge sensor capacitively coupled to the electron trap and adirectional coupler coupled to the charge sensor.
 13. The system ofclaim 12, further comprising: a resonant circuit coupled between thedirectional coupler and the charge sensor; an analog-to-digitalconverter (ADC) coupled to the directional coupler; and a clock coupledto the ADC.
 14. A method to implement a qubit, the method comprising:preparing a film of liquid helium, wherein the film of liquid helium issupporting an electron subsystem, wherein the electron subsystemcomprises electrons floating near a surface of the film of liquidhelium, and wherein the electrons are confined, in a directionperpendicular to the surface of the film of liquid helium, by imageforces of electrostatic attraction to the film of liquid helium;applying a first side gate voltage to a side gate to electrostaticallycreate a boundary of the electron subsystem; applying a first trap gatevoltage to a trap gate to electrostatically create an electron traplocated outside the boundary of the electron subsystem; opening accessof the electrons of the electron subsystem to the electron trap byapplying a first load gate voltage to a load gate to populate theelectron trap; and closing access of the electrons of the electronsubsystem to the electron trap by applying a second load gate voltage tothe load gate.
 15. The method of claim 14, further comprising adjustinga number of the electrons in the electron trap by applying a second trapgate voltage to the electron trap so that a pre-determined number of theelectrons remains in the electron trap.
 16. The method of claim 15,wherein the pre-determined number of the electrons is one.
 17. A methodto determine a state of a qubit, the method comprising: preparing afirst input signal having a frequency corresponding to a first energydifference between Eigenstates of the qubit; subjecting the qubit to thefirst input signal by delivering the first input signal to a microwaveresonator circuit wherein the microwave resonator circuit iscapacitively coupled to the qubit; detecting a first response of themicrowave resonator circuit to the first input signal; and determiningthe state of the qubit based on the first response of the microwaveresonator circuit to the first input signal.
 18. The method of claim 17,wherein preparing the first input signal comprises: generating a firstsignal having a first frequency; generating a second signal by mixingthe first signal with one or more phase-stable pulses generated by awaveform generator; and generating the first input signal byup-converting the second signal to a target frequency, wherein thetarget frequency corresponds to the first energy difference between theEigenstates of the qubit.
 19. The method of claim 18, wherein deliveringthe first input signal to the microwave resonator circuit comprisestransmitting the first input signal through a tapered waveguide.
 20. Themethod of claim 17, wherein delivering the first input signal into themicrowave resonator circuit comprises transmitting the first inputsignal through a coaxial cable.
 21. The method of claim 17, wherein themicrowave resonator circuit comprises a charge sensor capacitivelycoupled to the qubit.
 22. The method of claim 17, wherein determiningthe state of the qubit from the first response of the microwaveresonator circuit comprises passing the first response of the microwaveresonator circuit through an analog-to-digital converter.
 23. The methodof claim 17, further comprising: preparing a second input signal havinga second frequency corresponding to a second energy difference betweenEigenstates of the qubit; subjecting the qubit to the second inputsignal wherein the microwave resonator circuit is capacitively coupledto the qubit; and detecting a second response of the microwave resonatorcircuit to the second input signal; and wherein determining the state ofthe qubit is further based on the second response of the microwaveresonator circuit to the second input signal.
 24. The method claim 23,wherein the second input signal has a frequency at least ten times afrequency of the first input signal, and wherein the first input signalis delivered to the microwave resonator circuit through a coaxial cableand the second input signal is delivered to the microwave resonatorcircuit through a tapered waveguide.
 25. A method to determine a stateof a qubit of a plurality of qubits, the method comprising: capacitivelycoupling a device, comprising the plurality of qubits and a plurality ofcontrol gates, to a microwave resonator circuit, wherein each of theplurality of qubits is associated with a respective control gate of theplurality of control gates; receiving an indication that a targetedqubit is to be read out; applying a control voltage to the respectivecontrol gate associated with the targeted qubit to Stark-tune an energydifference between Eigenstates of the targeted qubit away from energydifferences between Eigenstates of other qubits; preparing an inputsignal having a frequency corresponding to the energy difference betweenthe Eigenstates of the targeted qubit; subjecting the device to theinput signal by delivering the input signal into the microwave resonatorcircuit; detecting a response of the microwave resonator circuit to aninput signal; and determining the state of the targeted qubit from theresponse of the microwave resonator circuit.
 26. The method of claim 25,wherein the plurality of qubits have a linear spatial arrangement or aplanar spatial arrangement.